Because of the unique selection rule, hyper-Raman scattering (HRS) can provide spectral information that linear Raman and infrared spectroscopy cannot obtain. However, the weak signal is the key bottleneck that restricts the application of HRS technique in study of the molecular structure, surface or interface behavior. Here, we theoretically design and investigate a kind of plasmonic substrate consisting of Ag nanorices for enhancing the HRS signal based on the electromagnetic enhancement mechanism. The Ag nanorice can excite multiple resonances at optical and near-infrared frequencies. By properly designing the structure parameters of Ag nanorice, multi- plasmon resonances with large electromagnetic field enhancements can be excited, when the "hot spots" locate on the same spatial positions and the resonance wavelengths match with the pump and the second-order Stokes beams, respectively. Assisted by the field enhancements resulting from the first- and second-longitudinal plasmon resonance of Ag nanorice, the enhancement factor of surface enhanced hyper-Raman scattering can reach as high as 5.08 × 109, meaning 9 orders of magnitude enhancement over the conventional HRS without the plasmonic substrate.